Science wars: Non-periodic crystals

Up until 1982, all crystals were believed to be, by definition, periodic. But then an Israeli materials scientist discovered something strange…

Quasicrystal
AMES lab., US Department of Energy, Public domain, via Wikimedia Commons

In January of last year, in a post about Girih tiles, I promised to write about non-periodic tiling and crystallography. So, today, we’re going to delve into the discovery of quasicrystals. As with all classic science stories, it begins with one scientist seemingly against the world.

First, a quick recap on non-periodic tiling. Some patterns repeat themselves in a predictable way. Think of a simple grid, for example. A grid pattern can extend itself endlessly in every direction, and it will always look the same no matter how far out you go.

(In technical terms, a grid is periodic and has translational symmetry. Say you took a picture of a grid, put it on a piece of transparent plastic, and then put that plastic on top of the original grid. It is possible to slide the plastic around – up, down, left, and right – and the two grids would always match up. This proves that there is a repeating, consistent pattern.)

There are some patterns, though, that do not have translational symmetry. Like the grid, they can extend endlessly in all directions, but they do not look the same as they do so. The most famous of these is Penrose tiling:

Penrose tiling
Inductiveload [Public domain]

Penrose tiling is aperiodic; you cannot slide the transparencies around and match them up.

What does all this have to do with crystallography? Well, crystals are essentially three-dimensional patterns. They repeat a very basic structure over and over. This begins at the atomic level with symmetrical patterns of atoms or molecules, and extends all the way to the large-scale shape of the crystal. Pyrite, for example, is a crystal that forms nearly perfect natural cubes:

Up until a few years ago, this was a core defining feature of crystals: they were periodic, the 3D equivalent of our grid example. But then, in 1982, an Israeli scientist working in Washington, DC, named Dan Shechtman found an alloy of aluminium and manganese that seemed to break that rule. It wasn’t a crystal as we knew it. Like Girih tiles or Penrose tiles, it extended in all directions but not periodically. It was a quasicrystal.

This result was so controversial, he didn’t publish it for two years. And, when he did, he drew an enormous amount of criticism from the scientific community. Not least from Linus Pauling, one of the most prestigious scientists of the 20th century. When the only person to win two un-shared Nobel Prizes says “there is no such thing as quasicrystals, only quasi-scientists” you have to feel a little isolated.

In any case, it turns out that Shechtman was right all along. Today we know of many different quasicrystals, including the handsome holmium–magnesium–zinc character pictured at the top of this post. For his work busting open the field of crystallography, Shechtman received a Nobel Prize of his own in 2011.

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